What is the integral of (7t^3+t^2)/(sqrt(t)) ?

The integral of (7t^3+t^2)/(sqrt(t)) is 2t^{7/2}+2/5 t^{5/2}+C

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integral of (7t^3+t^2)/(sqrt(t))

\int \frac{7 t ^{3} + t ^{2}}{t} d t

2 t^{\frac{7}{2}} + \frac{2}{5} t^{\frac{5}{2}} + C

Solution steps

\int \frac{7 t ^{3} + t ^{2}}{t} d t

Expand

\frac{7 t ^{3} + t ^{2}}{t} : \frac{7 t ^{3}}{t} + \frac{t ^{2}}{t}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{7 t ^{3}}{t} d t + \int \frac{t ^{2}}{t} d t

\int \frac{7 t ^{3}}{t} d t = 2 t^{\frac{7}{2}}

\int \frac{t ^{2}}{t} d t = \frac{2}{5} t^{\frac{5}{2}}

= 2 t^{\frac{7}{2}} + \frac{2}{5} t^{\frac{5}{2}}

Add a constant to the solution

= 2 t^{\frac{7}{2}} + \frac{2}{5} t^{\frac{5}{2}} + C

2^{8 - x^{2}}

\int \frac{1}{4 x ^{2} + 2} d x

n = 0 \sum \infty \frac{( n ^{n} )}{n !}

\int \frac{1}{z} d z

\frac{d}{d x} (3 x^{3} - x^{2} + 1)

What is the integral of (7t^3+t^2)/(sqrt(t)) ?
The integral of (7t^3+t^2)/(sqrt(t)) is 2t^{7/2}+2/5 t^{5/2}+C